|20||Bush > Gore > Nader|
|10||Gore > Bush > Nader|
|29||Nader > Gore > Bush|
In this 59-voter IRV (Instant Runoff Voting) election we've artificially named the candidates "Bush," "Gore" and "Nader" to remind you of the famous 2000 US presidential election in which Nader played a "spoiler" role causing Bush to win. We are not claiming this setup actually represents or resembles that election to any more than a slight degree.
Under the rules of IRV, Gore is eliminated and the Gore second-votes go to Bush, who wins over Nader 30-29.
But what if 10 (or more) people in the third group, realizing Nader has no chance, strategically decide to insincerely switch their first and second rankings (or just take Nader off their ballots)? It then looks like:
|20||Bush > Gore > Nader|
|20||Gore > Bush > Nader|
|19||Nader > Gore > Bush|
Now Bush and Gore get 20 first place votes apiece, and Nader only 19. Nader is eliminated first, giving 19 votes to Gore, and Gore crushingly beats Bush, 39-20. Those ten who switched their votes, got Gore (their second choice) instead of Bush (their third choice).
Betraying Nader paid off. IRV means betraying your true favorite third party candidate pays off. Voting third party can mean wasting your vote under IRV, just like under plurality. So voters do the betrayal. They don't want to waste their vote. So third party candidates lose by artificially large losses. So third parties die off. So two-party domination sets in.
Conclusion: IRV leads to self-reinforcing 2-party domination.
This is of course oversimplified in the sense that just one artificial simple election example just not necessarily prove that the net effect of all real world elections will be to cause 2-party domination with IRV. However, it really seems to be an experimental fact that all IRV countries have historically developed 2-party domination in IRV seats, for example in the Australian House (elected via IRV) zero third-party seat winners happened during the three election cycles 2004-2007-2010, comprising 450 seat-races in all. (The NatLibs and Labour are the two top parties, although the begginer can be somewhat confused by the fact that, due to Australian history, various parties merged or effectively merged...) Computer simulations show that Favorite Betrayal scenarios arise in 3-candidate IRV random elections about 19.6% of the time with perfect knowledge. [With (more realistically) imperfect knowledge, arguably they arise 100% of the time, although that would e a highly debatable argument.]
Another slightly more complicated example intended to be more realistic (this one was intended to be simple).
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